結果
| 問題 | No.1145 Sums of Powers |
| ユーザー |
 hotman78
|
| 提出日時 | 2020-07-31 21:25:44 |
| 言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,135 ms / 2,000 ms |
| コード長 | 14,641 bytes |
| コンパイル時間 | 22,811 ms |
| コンパイル使用メモリ | 452,348 KB |
| 最終ジャッジ日時 | 2025-01-12 08:59:34 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 6 |
ソースコード
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC push_options
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#include<bits/stdc++.h>
#include <xmmintrin.h>
#include <immintrin.h>
using namespace::std;
__attribute__((constructor))void init(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/priority_queue.hpp>
#include<ext/pb_ds/tag_and_trait.hpp>
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// typedef mp::number<mp::cpp_dec_float<0>> cdouble;
// typedef mp::cpp_int cint;
template<typename T>using pbds=__gnu_pbds::tree<T,__gnu_pbds::null_type,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T>using pbds_map=__gnu_pbds::tree<T,T,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T,typename E>using hash_map=__gnu_pbds::gp_hash_table<T,E>;
template<typename T>using pqueue =__gnu_pbds::priority_queue<T, greater<T>,__gnu_pbds::rc_binomial_heap_tag>;
typedef long long lint;
#define INF (1LL<<60)
#define IINF (1<<30)
#define LINF (9223372036854775807LL)
#define EPS (1e-10)
#define endl ('\n')
//#define MOD 1000000007LL
#define MOD 998244353LL
//#define MOD 18446744069414584321ULL
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template<typename T>inline void numout(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i<INF/2?i:"INF";f=1;}cout<<endl;}
template<typename T>inline void numout2(T t){for(auto i:t)numout(i);}
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void _output(T t){bool f=0;for(lint i=0;i<t.size();i++){cout<<f?"":" "<<t[i];f=1;}cout<<endl;}
template<typename T>inline void _output2(T t){for(lint i=0;i<t.size();i++)output(t[i]);}
#define rep(i,...) for(auto i:range(__VA_ARGS__))
#define rrep(i,...) for(auto i:reversed(range(__VA_ARGS__)))
#define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i)
#define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i)
#define irep(i) for(lint i=0;;++i)
inline vector<int64_t> range(int64_t n){vector<int64_t>v(n);iota(v.begin(),v.end(),0LL);return v;}
inline vector<int64_t> range(int64_t a,int64_t b){vector<int64_t>v(b-a);iota(v.begin(),v.end(),a);return v;}
inline vector<int64_t> range(int64_t a,int64_t b,int64_t c){vector<int64_t>v((b-a+c-1)/c);for(int i=0;i<(int)v.size();++i)v[i]=i?v[i-1]+c:a;return v;}
inline auto reversed(auto v){reverse(v.begin(),v.end());return v;}
#define all(n) begin(n),end(n)
#define dist(a,b,c,d) sqrt(pow(a-c,2)+pow(b-d,2))
//inline lint gcd(lint A,lint B){return B?gcd(B,A%B):A;}
//inline lint lcm(lint A,lint B){return A/gcd(A,B)*B;}
// inline cint cgcd(cint A,cint B){return B?cgcd(B,A%B):A;}
// inline cint clcm(cint A,cint B){return A/cgcd(A,B)*B;}
bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;}
bool chmax(auto& s,const auto& t){bool res=s<t;s=max(s,t);return res;}
const vector<lint> dx={1,0,-1,0,1,1,-1,-1};
const vector<lint> dy={0,1,0,-1,1,-1,1,-1};
#define SUM(v) accumulate(all(v),0LL)
auto call=[](auto f,auto... args){return f(f,args...);};
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}
template<typename T,typename P>
struct FPS_BASE:vector<T>{
using vector<T>::vector;
inline P operator +(T x)noexcept{return P(*static_cast<P*>(this))+=x;}
inline P operator -(T x)noexcept{return P(*static_cast<P*>(this))-=x;}
inline P operator *(T x)noexcept{return P(*static_cast<P*>(this))*=x;}
inline P operator /(T x)noexcept{return P(*static_cast<P*>(this))/=x;}
inline P operator <<(int x)noexcept{return P(*static_cast<P*>(this))<<=x;}
inline P operator >>(int x)noexcept{return P(*static_cast<P*>(this))>>=x;}
inline P operator +(const P& x)noexcept{return P(*static_cast<P*>(this))+=x;}
inline P operator -(const P& x)noexcept{return P(*static_cast<P*>(this))-=x;}
inline P operator -()noexcept{return P(1,T(0))-=P(*static_cast<P*>(this));}
inline P operator *(const P& x)noexcept{return P(*static_cast<P*>(this))*=x;}
inline P operator /(const P& x)noexcept{return P(*static_cast<P*>(this))/=x;}
inline P operator %(const P& x)noexcept{return P(*static_cast<P*>(this))%=x;}
inline P &operator +=(T x){
if(this->size()==0)this->resize(1,T(0));
(*static_cast<P*>(this))[0]+=x;
return (*static_cast<P*>(this));
}
inline P &operator -=(T x){
if(this->size()==0)this->resize(1,T(0));
(*static_cast<P*>(this))[0]-=x;
return (*static_cast<P*>(this));
}
inline P &operator *=(T x){
for(int i=0;i<(int)this->size();++i){
(*static_cast<P*>(this))[i]*=x;
}
return (*static_cast<P*>(this));
}
inline P &operator /=(T x){
return (*static_cast<P*>(this))*=(T(1)/x);
}
inline P &operator <<=(int x){
P ret(x,T(0));
ret.insert(ret.end(),begin(*static_cast<P*>(this)),end(*static_cast<P*>(this)));
return (*static_cast<P*>(this))=ret;
}
inline P &operator >>=(int x){
P ret;
ret.insert(ret.end(),begin(*static_cast<P*>(this))+x,end(*static_cast<P*>(this)));
return (*static_cast<P*>(this))=ret;
}
inline P &operator +=(const P& x){
if(this->size()<x.size())this->resize(x.size(),T(0));
for(int i=0;i<(int)x.size();++i){
(*this)[i]+=x[i];
}
return (*static_cast<P*>(this));
}
inline P &operator -=(const P& x){
if(this->size()<x.size())this->resize(x.size(),T(0));
for(int i=0;i<(int)x.size();++i){
(*static_cast<P*>(this))[i]-=x[i];
}
return (*static_cast<P*>(this));
}
inline P &operator *=(const P& x){
return (*static_cast<P*>(this))=mul((*static_cast<P*>(this)),x);
}
inline P &operator /=(P x){
if(this->size()<x.size()) {
this->clear();
return (*static_cast<P*>(this));
}
const int n=this->size()-x.size()+1;
return (*static_cast<P*>(this)) = (rev().pre(n)*x.rev().inv(n)).pre(n).rev(n);
}
inline P &operator %=(const P& x){
return ((*static_cast<P*>(this))-=*static_cast<P*>(this)/x*x);
}
inline P& shrink(){while((*static_cast<P*>(this)).back()==0)(*static_cast<P*>(this)).pop_back();return (*static_cast<P*>(this));}
inline P pre(int sz)const{
return P(begin(*this),begin(*this)+min((int)this->size(),sz));
}
inline P rev(int deg=-1){
P ret(*static_cast<P*>(this));
if(deg!=-1)ret.resize(deg,T(0));
reverse(begin(ret),end(ret));
return ret;
}
P inv(int deg=-1){
assert((*static_cast<P*>(this))[0]!=T(0));
const int n=deg==-1?this->size():deg;
P ret({T(1)/(*this)[0]});
for(int i=1;i<n;i<<=1){
ret=(ret*T(2)-ret*ret*pre(i<<1)).pre(i<<1);
}
return ret.pre(n);
}
inline P dot(const P& x){
P ret(*static_cast<P*>(this));
for(int i=0;i<int(min(this->size(),x.size()));++i){
ret[i]*=x[i];
}
return ret;
}
P diff(){
P ret(*static_cast<P*>(this));
for(int i=0;i<(int)ret.size();i++){
ret[i]*=i;
}
return ret>>1;
}
P integral(){
P ret(*static_cast<P*>(this));
for(int i=0;i<(int)ret.size();i++){
ret[i]/=i+1;
}
return ret<<1;
}
P log(int deg=-1){
assert((*this)[0]==T(1));
const int n=deg==-1?this->size():deg;
return (diff()*inv(n)).pre(n-1).integral();
}
P exp(int deg=-1){
assert((*this)[0]==T(0));
const int n=deg==-1?this->size():deg;
P ret({T(1)});
for(int i=1;i<n;i<<=1){
ret=ret*(pre(i<<1)+1-ret.log(i<<1)).pre(i<<1);
}
return ret.pre(n);
}
P sqrt(int deg=-1){
const int n=deg==-1?this->size():deg;
if((*this)[0]==T(0)) {
for(int i=1;i<(int)this->size();i++) {
if((*this)[i]!=T(0)) {
if(i&1)return{};
if(n-i/2<=0)break;
auto ret=(*this>>i).sqrt(n-i/2)<<(i/2);
if((int)ret.size()<n)ret.resize(n,T(0));
return ret;
}
}
return P(n,0);
}
P ret({T(1)});
for(int i=1;i<n;i<<=1){
ret=(ret+pre(i<<1)*ret.inv(i<<1)).pre(i<<1)/T(2);
}
return ret.pre(n);
}
T eval(T x){
T res=0;
for(int i=(int)this->size()-1;i>=0;--i){
res*=x;
res+=(*this)[i];
}
return res;
}
vector<T> multipoint_eval(const vector<T>&x){
const int n=x.size();
P* v=new P[2*n-1];
for(int i=0;i<n;i++)v[i+n-1]={T()-x[i],T(1)};
for(int i=n-2;i>=0;i--){v[i]=v[i*2+1]*v[i*2+2];}
v[0]=P(*static_cast<P*>(this))%v[0];v[0].shrink();
for(int i=1;i<n*2-1;i++){
v[i]=v[(i-1)/2]%v[i];
v[i].shrink();
}
vector<T>res(n);
for(int i=0;i<n;i++)res[i]=v[i+n-1][0];
return res;
}
virtual P mul(P s,P t)=0;
};
template<typename Mint>
struct fps9:FPS_BASE<Mint,fps9<Mint>>{
using FPS_BASE<Mint,fps9<Mint>>::FPS_BASE;
using P=fps9<Mint>;
P mul(P s,P t)override{
const int n=s.size()+t.size()-1;
int h=1;
while((1<<h)<n)h++;
s.resize((1<<h),Mint(0));
t.resize((1<<h),Mint(0));
return ntt(ntt(s,h,0).dot(ntt(t,h,0)),h,1).pre(n);
}
P ntt(P v,const int& h,const bool& inv){
const int n=v.size();
assert(Mint::get_mod()>=3&&Mint::get_mod()%2==1);
P tmp(n,Mint());
Mint root=inv?Mint(Mint::root()).inv():Mint::root();
for(int b=n>>1;b>=1;b>>=1,v.swap(tmp)){
Mint w=root.pow((Mint::get_mod()-1)/(n/b)),p=1;
for(int i=0;i<n;i+=b*2,p*=w)for(int j=0;j<b;++j){
v[i+j+b]*=p;
tmp[i/2+j]=v[i+j]+v[i+b+j];
tmp[n/2+i/2+j]=v[i+j]-v[i+b+j];
}
}
if(inv)v/=n;
return v;
}
};
class mint {
using u64 = std::uint_fast64_t;
public:
u64 a;
constexpr mint(const long long x = 0)noexcept:a(x>=0?x%get_mod():get_mod()-(-x)%get_mod()){}
constexpr u64 &value()noexcept{return a;}
constexpr const u64 &value() const noexcept {return a;}
constexpr mint operator+(const mint rhs)const noexcept{return mint(*this) += rhs;}
constexpr mint operator-(const mint rhs)const noexcept{return mint(*this)-=rhs;}
constexpr mint operator*(const mint rhs) const noexcept {return mint(*this) *= rhs;}
constexpr mint operator/(const mint rhs) const noexcept {return mint(*this) /= rhs;}
constexpr mint &operator+=(const mint rhs) noexcept {
a += rhs.a;
if (a >= get_mod())a -= get_mod();
return *this;
}
constexpr mint &operator-=(const mint rhs) noexcept {
if (a<rhs.a)a += get_mod();
a -= rhs.a;
return *this;
}
constexpr mint &operator*=(const mint rhs) noexcept {
a = a * rhs.a % get_mod();
return *this;
}
constexpr mint operator++(int n) noexcept {
a += 1;
if (a >= get_mod())a -= get_mod();
return *this;
}
constexpr mint operator--(int n) noexcept {
if (a<1)a += get_mod();
a -= 1;
return *this;
}
constexpr pair<int, int> extgcd(int a, int b) {
int s = a, sx = 1, sy = 0, t = b, tx = 0, ty = 1;
while (s % t != 0) {
int temp = s / t;
int u = s - t * temp;
int ux = sx - tx * temp;
int uy = sy - ty * temp;
s = t;
sx = tx;
sy = ty;
t = u;
tx = ux;
ty = uy;
}
return {tx, ty};
}
constexpr mint &operator/=(mint rhs) noexcept {
return (*this)*=mint(extgcd(rhs.a,get_mod()).first);
}
constexpr bool operator==(mint x) noexcept {
return a==x.a;
}
constexpr bool operator!=(mint x) noexcept {
return a!=x.a;
}
constexpr static int root(){
mint root = 2;
while(root.pow((get_mod()-1)>>1).a==1)root++;
return root.a;
}
constexpr mint pow(long long n){
long long x=a;
mint ret = 1;
while(n>0) {
if(n&1)(ret*=x);
(x*=x)%=get_mod();
n>>=1;
}
return ret;
}
constexpr mint inv(){
return pow(get_mod()-2);
}
static vector<mint> fac,ifac;
static bool init;
constexpr static int mx=10000001;
void build(){
init=0;
fac.resize(mx);
ifac.resize(mx);
fac[0]=1,ifac[0]=1;
for(int i=1;i<mx;i++)fac[i]=fac[i-1]*i;
ifac[mx-1]=fac[mx-1].inv();
for(int i=mx-2;i>=0;i--)ifac[i]=ifac[i+1]*(i+1);
}
mint comb(lint b){
if(init)build();
if(a==0&&b==0)return 1;
if((lint)a<b||a<0)return 0;
return fac[a]*ifac[a-b]*ifac[b];
}
mint fact(){
if(init)build();
return fac[a];
}
mint fact_inv(){
if(init)build();
return ifac[a];
}
friend ostream& operator<<(ostream& lhs, const mint& rhs) noexcept {
lhs << rhs.a;
return lhs;
}
friend istream& operator>>(istream& lhs,mint& rhs) noexcept {
lhs >> rhs.a;
return lhs;
}
constexpr static u64 get_mod(){return MOD;}
};
vector<mint> mint::fac;
vector<mint> mint::ifac;
bool mint::init=1;
int main(){
lint n,k;
cin>>n>>k;
vec a(n);
rep(i,n)cin>>a[i];
vector<pair<fps9<mint>,fps9<mint>>>c(2*n-1);
rep(i,n){
c[i+n-1]=make_pair(fps9<mint>{1},fps9<mint>{1,-a[i]});
}
auto merge=[&](auto s,auto t){
return make_pair(s.first*t.second+s.second*t.first,s.second*t.second);
};
rrep(i,n-1){
c[i]=merge(c[i*2+1],c[i*2+2]);
}
auto e=(c[0].first*(c[0].second.inv(k+1))).pre(k+1);
vector<mint> ans(k);
rep(i,1,k+1){
ans[i-1]=e[i];
}
output(ans);
}